If X follows a binomial distribution with n = 6 and then the skewness of X is:

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )

Answer 1

Given

n = 6

p = 1/4

Formula

S_k = (1 - 2p)/√(np(1 - p)

Calculation

Skewness of X = (1 - 2 × 1/4)/√(6 × 1/4(1 - 1/4)

⇒ (1 - 1/2(/√(3/2 × 3/4

⇒ 1/2/√(9/8)

∴ The value of skewness X is√2/3

Binomial distribution = A random variable X has a binomial distribution if its probability distribution is given by

b(x; n, p) = P(X = x) = (n x)p^xq^{n - x} x = 0, 1, 2, ----n

Normal distribution has the probability density function given by

f(x) = [1/(σ√2π)]e^{1/2(x - μ/σ)}²

Here, μ and σ are prameters of this distribution. The parameter μ is mean and σ is square root of variance of this distribution

-∞ < μ < ∞, σ > 0

The normal distribution is also called as the Gaussian distribution